The Field Reversed Configuration (FRC) belongs to the class of magnetic plasma confinement topologies known as compact toroids (CT). It exhibits predominantly poloidal magnetic fields and possesses zero or small self-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033 (1988)). The attractions of such a configuration are its simple geometry for ease of construction and maintenance, a natural unrestricted divertor for facilitating energy extraction and ash removal, and very high β (β is the ratio of the average plasma pressure to the average magnetic field pressure inside the FRC), i.e., high power density. The high β nature is advantageous for economic operation and for the use of advanced, aneutronic fuels such as D-He3 and p-B11.
The traditional method of forming an FRC uses the field-reversed θ-pinch technology, producing hot, high-density plasmas (see A. L. Hoffman and J. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is the translation-trapping method in which the plasma created in a theta-pinch “source” is more-or-less immediately ejected out one end into a confinement chamber. The translating plasmoid is then trapped between two strong mirrors at the ends of the chamber (see, for instance, H. Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191 (1995)). Once in the confinement chamber, various heating and current drive methods may be applied such as beam injection (neutral or neutralized), rotating magnetic fields, RF or ohmic heating, etc. This separation of source and confinement functions offers key engineering advantages for potential future fusion reactors. FRCs have proved to be extremely robust, resilient to dynamic formation, translation, and violent capture events. Moreover, they show a tendency to assume a preferred plasma state (see e.g. H. Y. Guo, A. L. Hoffman, K. E. Miller, and L. C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significant progress has been made in the last decade developing other FRC formation methods: merging spheromaks with oppositely-directed helicities (see e.g. Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl. Fusion 39, 2001 (1999)) and by driving current with rotating magnetic fields (RMF) (see e.g. I. R. Jones, Phys. Plasmas 6, 1950 (1999)) which also provides additional stability.
Recently, the collision-merging technique, proposed long ago (see e.g. D. R. Wells, Phys. Fluids 9, 1010 (1966)) has been significantly developed further: two separate theta-pinches at opposite ends of a confinement chamber simultaneously generate two plasmoids and accelerate the plasmoids toward each other at high speed; they then collide at the center of the confinement chamber and merge to form a compound FRC. In the construction and successful operation of one of the largest FRC experiments to date, the conventional collision-merging method was shown to produce stable, long-lived, high-flux, high temperature FRCs (see e.g. M. Binderbauer, H. Y. Guo, M. Tuszewski et al., Phys. Rev. Lett. 105, 045003 (2010)).
FRCs consist of a torus of closed field lines inside a separatrix, and of an annular edge layer on the open field lines just outside the separatrix. The edge layer coalesces into jets beyond the FRC length, providing a natural divertor. The FRC topology coincides with that of a Field-Reversed-Mirror plasma. However, a significant difference is that the FRC plasma has a β of about 10. The inherent low internal magnetic field provides for a certain indigenous kinetic particle population, i.e. particles with large larmor radii, comparable to the FRC minor radius. It is these strong kinetic effects that appear to at least partially contribute to the gross stability of past and present FRCs, such as those produced in the collision-merging experiment.
Typical past FRC experiments have been dominated by convective losses with energy confinement largely determined by particle transport. Particles diffuse primarily radially out of the separatrix volume, and are then lost axially in the edge layer. Accordingly, FRC confinement depends on the properties of both closed and open field line regions. The particle diffusion time out of the separatrix scales as τ⊥˜a2/D⊥ (a·rs/4, where rs is the central separatrix radius), and D⊥ is a characteristic FRC diffusivity, such as D⊥˜12.5 ρie, with ρie representing the ion gyroradius, evaluated at an externally applied magnetic field. The edge layer particle confinement time τ∥ is essentially an axial transit time in past FRC experiments. In steady-state, the balance between radial and axial particle losses yields a separatrix density gradient lengths δ˜(D⊥τ∥)1/2. The FRC particle confinement time scales as (τ⊥τ∥)1/2 for past FRCs that have substantial density at the separatrix (see e.g. M. Tuszewski, “Field Reversed Configurations,” Nucl. Fusion 28, 2033 (1988)).
Another drawback of prior FRC system designs was the need to use external multipoles to control rotational instabilities such as the fast growing n=2 interchange instabilities. In this way the typical externally applied quadrupole fields provided the required magnetic restoring pressure to dampen the growth of these unstable modes. While this technique is adequate for stability control of the thermal bulk plasma, it poses a severe problem for more kinetic FRCs or advanced hybrid FRCs, where a highly kinetic large orbit particle population is combined with the usual thermal plasma. In these systems, the distortions of the axisymmetric magnetic field due to such multipole fields leads to dramatic fast particle losses via collisionless stochastic diffusion, a consequence of the loss of conservation of canonical angular momentum. A novel solution to provide stability control without enhancing diffusion of any particles is, thus, important to take advantage of the higher performance potential of these never-before explored advanced FRC concepts.
In light of the foregoing, it is, therefore, desirable to improve the confinement and stability of FRCs in order to use steady state FRCs as a pathway to a whole variety of applications from compact neutron sources (for medical isotope production and nuclear waste remediation), to mass separation and enrichment systems, and to a reactor core for fusion of light nuclei for the future generation of energy.